贝叶斯分类器MATLAB经典程序

function Bayes2

%为了提高实验样本测试的精度，故采用多次模拟求平均值的方法

N=input('实验模拟次数N(N最好为奇数)＝');

Result(1:3,1:3)=0; %判别矩阵的初始化

for k=1:N %控制程序模拟次数N

%生成二维正态分布的样本2 X N 维的矩阵

X1=mvnrnd([1 2],[4 0;0 6],300)'; %2 X N

X2=mvnrnd([5 3],[5 0;0 1],200)';

X3=mvnrnd([4 7],[2 0;0 9],500)'; %样本程序

%---------------------------------------------------%

%测试样本

X10=mvnrnd([1 2],[4 0;0 6],100)'; %2 X N

X20=mvnrnd([5 3],[5 0;0 1],100)';

X30=mvnrnd([4 7],[2 0;0 9],100)';

%先验概率

P(1)=length(X1)/(length(X1)+length(X2)+length(X3));

P(2)=length(X2)/(length(X1)+length(X2)+length(X3));

P(3)=length(X3)/(length(X1)+length(X2)+length(X3));

%计算相关量cov(X)：协方差矩阵Ave:均值

%--------------------------------------------------------%

W1=-1/2*inv(cov(X1')); W2=-1/2*inv(cov(X2')); W3=-1/2*inv(cov(X3'));%

Ave1=(sum(X1')/length(X1))';Ave2=(sum(X2')/length(X2))';

Ave3=(sum(X3')/length(X3))';%计算平均值(2维列向量)

w1=inv(cov(X1'))*Ave1;w2=inv(cov(X2'))*Ave2;w3=inv(cov(X3'))* Ave3;%2

w10=-1/2*Ave1'*inv(cov(X1'))*Ave1-1/2*log(det(cov(X1')))+log(P(1 ));

w20=-1/2*Ave2'*inv(cov(X2'))*Ave2-1/2*log(det(cov(X2')))+log(P(2 ));

w30=-1/2*Ave3'*inv(cov(X3'))*Ave3-1/2*log(det(cov(X3')))+log(P(3 ));

%-----------------------------------------------------------%

for i=1:3

for j=1:100

if i==1

g1=X10(:,j)'*W1*X10(:,j)+w1'*X10(:,j)+w10;

g2=X10(:,j)'*W2*X10(:,j)+w2'*X10(:,j)+w20;

g3=X10(:,j)'*W3*X10(:,j)+w3'*X10(:,j)+w30;

if g1>=g2&g1>=g3

Result(1,1)=Result(1,1)+1;

elseif g2>=g1&g2>=g3

Result(1,2)=Result(1,2)+1;%记录误判情况

else

Result(1,3)=Result(1,3)+1;%记录误判情况

end

elseif i==2

g1=X20(:,j)'*W1*X20(:,j)+w1'*X20(:,j)+w10;

g2=X20(:,j)'*W2*X20(:,j)+w2'*X20(:,j)+w20;

g3=X20(:,j)'*W3*X20(:,j)+w3'*X20(:,j)+w30;

if g2>=g1&g2>=g3

Result(2,2)=Result(2,2)+1;

elseif g1>=g2&g1>=g3

Result(2,1)=Result(2,1)+1;

else

Result(2,3)=Result(2,3)+1;

end

else

g1=X30(:,j)'*W1*X30(:,j)+w1'*X30(:,j)+w10;

g2=X30(:,j)'*W2*X30(:,j)+w2'*X30(:,j)+w20;

g3=X30(:,j)'*W3*X30(:,j)+w3'*X30(:,j)+w30;

if g3>=g1&g3>=g2

Result(3,3)=Result(3,3)+1;

elseif g2>=g1&g2>=g3

Result(3,2)=Result(3,2)+1;

else

Result(3,1)=Result(3,1)+1;

end

end

end

end

end

%画出各样本的分布情况

subplot(2,1,1)

plot(X1(1,:),X1(2,:),'r.','LineWidth',2),hold on

plot(X2(1,:),X2(2,:),'go','LineWidth',2),hold on

plot(X3(1,:),X3(2,:),'b+','LineWidth',2),hold on

title('训练样本分布情况')

legend('训练样本1','训练样本2','训练样本3') subplot(2,1,2)

plot(X10(1,:),X10(2,:),'r.','LineWidth',2),hold on

plot(X20(1,:),X20(2,:),'go','LineWidth',2),hold on

plot(X30(1,:),X30(2,:),'b+','LineWidth',2),hold on

title('测试样本分布情况')